Fermat’s Last Theorem. Simon Singh

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      The story of Fermat had ended in the most spectacular fashion. For Andrew Wiles, it meant the end of professional isolation of a kind almost alien to maths, which is usually a collaborative activity. Ritual afternoon tea in mathematics institutes the world over is a time when ideas come together, and sharing insight before publication is the norm. Ken Ribet, a mathematician who was himself central to the proof, only half jokingly suggested to me that it is the insecurity of mathematicians that requires the support structure of their colleagues. Andrew Wiles had eschewed all that, and kept his work to himself in all but the final stages. That too was a measure of the importance of Fermat. He had a real driving passion to be the one who solved this problem, a passion strong enough to devote seven years of his life and keep his goal to himself. He had known that however irrelevant the problem had seemed, competition for Fermat had never lessened, and he could never have risked revealing what he was doing.

      After weeks of researching the field, I had arrived in Princeton. For mathematicians, the level of emotion was intense. I had found a story of competition, success, isolation, genius, triumph, jealousy, intense pressure, loss and even tragedy. At the heart of that crucial Taniyama-Shimura Conjecture lay the tragic post-war life in Japan of Yutaka Taniyama, whose story I was privileged to hear from his close friend Goro Shimura. From Shimura too I learned of the notion of ‘goodness’ in maths, where things simply feel right, because they are good. Somehow, the sense of goodness pervaded the atmosphere of mathematics that summer. All were revelling in the glorious moment.

      With all this in train, small wonder at the weight of responsibility that Andrew felt as the flaw had gradually emerged over the autumn of 1993. With the eyes of the world upon him, and his colleagues calling to have the proof made public, somehow, and only he knows how, he didn’t crack. He had moved from doing maths in privacy and at his own pace to suddenly working in public. Andrew is an intensely private man, who fought hard to keep his family sheltered from the storm that was breaking around him. Throughout that week while I was in Princeton, I called, I left notes at his office, on his doorstep, and with his friends; I even provided a gift of English tea and Marmite. But he resisted my overtures, until that chance meeting on the day of my departure. A quiet, intense conversation followed, that in the end lasted barely fifteen minutes.

      When we parted that afternoon there was an understanding between us. If he managed to repair the proof, then he would come to me to discuss a film; I was prepared to wait. But as I flew home to London that night it seemed to me that the television programme was dead. No one had ever repaired a hole in the many attempted proofs of Fermat in three centuries. History was littered with false claims, and much as I wished that he would be the exception, it was hard to imagine Andrew as anything but another headstone in that mathematical graveyard.

      A year later I received the call. After an extraordinary mathematical twist, and a flash of true insight and inspiration, Andrew had finally brought an end to Fermat in his professional life. A year after that, we found the time for him to devote to filming. By this time I had invited Simon Singh to join me in making the film, and together we spent time with Andrew, learning from the man himself the full story of those seven years of isolated study, and his year of hell that followed. As we filmed, Andrew told us, as he had told no one before, of his innermost feelings about what he had done; how for thirty years he had hung on to a childhood dream; how so much of the maths he had ever studied had been, without his really knowing it at the time, really a gathering of tools for the Fermat challenge that had dominated his career; how nothing would ever be the same; of his sense of loss for the problem that would no longer be his constant companion; and of the uplifting sense of release that he now felt. For a field in which the subject matter is technically about as difficult for a lay audience to understand as can be imagined, the level of emotional charge in our conversations was greater than any I have experienced in a career in science film making. For Andrew it was the end of a chapter in his life. For me it was a privilege to be close to it.

      The film was transmitted on BBC Television as Horizon: Fermat’s Last Theorem. Simon Singh has now developed those insights and intimate conversations, together with the full richness of the Fermat story and the history and mathematics that have always hung around it, into this book, which is a complete and enlightening record of one of the greatest stories in human thinking.

      John Lynch

      Editor of BBC TV’s Horizon series March 1997